Bayesian Conditional Monte Carlo Algorithms for Nonlinear Time-Series State Estimation

• Published in: IEEE transactions on signal processing Vol. 63; no. 14; pp. 3586 - 3598
• Main Authors: Petetin, Yohan, Desbouvries, Francois
• Format: Journal Article
• Language: English
• Published: New York IEEE 15.07.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation algorithms; Approximation methods; Bayes methods; Bayesian filtering; Computational modeling; conditional Monte Carlo (CMC); Economic models; hidden Markov models; jump Markov state-space systems (JMSS); Monte Carlo simulation; multiobject filtering; Numerical models; Probability Hypothesis Density; Rao-Blackwell particle filters; Signal processing algorithms; Smoothing methods
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2015.2423251

Bayesian filtering aims at estimating sequentially a hidden process from an observed one. In particular, sequential Monte Carlo (SMC) techniques propagate in time weighted trajectories which represent the posterior probability density function (pdf) of the hidden process given the available observations. On the other hand, conditional Monte Carlo (CMC) is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable. In this paper, we show that up to some adaptations, one can make use of the time recursive nature of SMC algorithms in order to propose natural temporal CMC estimators of some point estimates of the hidden process, which outperform the associated crude Monte Carlo (MC) estimator whatever the number of samples. We next show that our Bayesian CMC estimators can be computed exactly, or approximated efficiently, in some hidden Markov chain (HMC) models; in some jump Markov state-space systems (JMSS); as well as in multitarget filtering. Finally our algorithms are validated via simulations.